In a word, time.
Timing is the most stressful part of buying a home and closing on a construction loan at the same time? Because a construction is based on the completed project, an appraisal needs to be done based on the project. That means you need to have a completed set of plans and a firm budget for the appraisal to do the appraisal. You want to give yourself at least 30 days prior to closing to have the completed set of plans and budget.
Of course it takes time get get plans and a budget completed. You need to select a builder and the builder and the project needs to be sent out for bid. That takes time as well especially since you don’t have easy access to the new property yet since you don’t own it until you close.
My recommendation is to only try to close on both the house and construction loan if you have 60-90 days to close. If the plans and budget are already done, it can certainly be done quicker.
As an alternative, you may want to consider closing on the property first, get the plans and budget done properly, and close on the construction after that.